examples: 13 1+3=4 13-4=9
94 9+4=13 94-13=81 8+1=9
156 1+5+6=12 156-12=144 1+4+4=9
And no matter what the size of the number it always goes back to 9!

1,233,465,957 add up to 45 4+5=9
- 45=
1,233,465,912=add all up =36 3+6=9
Can someone explain who invented numbers and why 9 is hidden in mathematical solving problems?

The number 9 is not supernatural. Certain spiritual, religious, and occult teachings claim that numbers have special meaning when in fact they do not. For example, if God is a Trinity, the Father, the Son, and the Holy Spirit, that does not make the number 3 supernatural.

The examples you list demonstrate a number theoretical property of the base 10 or decimal number system.

Base 10 is commonly used in mathematics and throughout society out of habit. There is nothing sacred about base 10. It became popular a long time ago simply because people counted on their fingers, and most people have 10 fingers.

What determines the base is the number of single character numbers used and what multiple character numbers represent. In base 10, there are 10 such single character numbers: 0,1,2,3,4,5,6,7,8, and 9. The next number greater than 9 is called 10, which is 0X1 + 1 X10. The number 472 = 2X1 + 7X10 + 4X10X10.

Other bases exist. Any whole number greater than 1 can define a base. For example, all computers operate on base 2 or binary mathematics. The 2 characters used are 0 and 1. This is the case because a single transistor can be in only one of two possible states, on or off. In this case, the number after 1 is 10, which can be converted to base 10 as 0X1 + 1X2 = 2. The number 11001 = 1X1 + 0X2 + 0X2X2 + 1X2X2X2 + 1X2X2X2X2 = 25 in base 10.

Digital circuits are often worked with in groups of 8, called a byte, to make it easier to code and decode data. So base 8 or octal mathematics can be used. The 8 single character numbers used are 0,1,2,3,4,5,6, and 7. The number after 7 is 10, which, converted to base 10, is the same as 0X1 + 1X8 = 8. The number 142 = 2X1 + 4X8 + 1X8X8 = 97 in base 10.

Sometimes 2 bytes, or 16 bits, are grouped together to simplify working with computerized data. Not surprisingly, base 16 or hexidecimal mathematics is used. The 16 single character numbers are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, and F. The number after F is 10, which can be converted to base 10 as 0X1 + 1X16 = 16. The number A5D03E = 14X1 + 3X16 + 0X16X16 + 13X16X16X16 + 5X16X16X16X16 + 10X16X16X16X16X16 = 10,866,750 in base 10.

In the same way any whole number such as 3, 4, 5, 22, 64, 183 or 122,835 could be used as the base of a number system. In fact, ancient Babylonia used a base 60 number system, and this is still commonly used to measure cirlces (360 degrees) and time (60 seconds and 60 minutes).

Getting back to your examples: “And no matter what the size of the number it always goes back to 9!” You are observing a number theoretical property of whole numbers, and “it always goes back to 9” only if you are working in a base 10 number system. There is nothing special about the number 9! If you are working in base 2, it always goes back to 0, in base 8 it always goes back to 7, and in base 16 it always goes back to F. I have verified that this is true, and I encourage you to do the same.

I repeat, there is nothing sacred about the base 10 number system. It was created by humans as an outgrowth of counting on fingers, and its continued use today is merely a convention.

If you are interested in studying these topics further, perform searches on “number theory” and “history of mathematics”. Both subjects are very interesting.